well, I solved it, but I must have made an error somewhere because I am not getting any of the giving values.
#help-28
austere cove
oblique swallow
well, I solved it, but I must have made an error somewhere because I am not gett...
can I get ur solution please?
austere cove
we are removing a factor of det(M^3) because it just makes the numbers larger.
!noans
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oblique swallow
we are removing a factor of det(M^3) because it just makes the numbers larger.
no no
I meant like
1s
oblique swallow
we are removing a factor of det(M^3) because it just makes the numbers larger.
We can get a cubic and then we can calculate the trace right?
austere cove
no need.
austere cove
!nosols
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austere cove
We can get a cubic and then we can calculate the trace right?
I have no idea what this equation is used for, but isn't that just x^3 - tr(A)x^2 + tr(A)x - det(A) = 0?
why do you have trace used twice?
oblique swallow
why do you have trace used twice?
misprint
mb
the stackexchange had a misprint
oblique swallow
so I'll walk through the steps I took
yes pls sir
austere cove
first I found the det(M), this happens to not be dependent on a.
so it's just a number
oblique swallow
okie
oblique swallow
ok so we want to find det(the formula) = 0
right
austere cove
we have that det(M) is just a number, so det(M^3) is similarly just a number. We can factor out det(M^3) to reduce the degree of everything.
so we're left with det(M^2 - 3M - 2aM + 8aI - 4I) = 0
we just calculate this matrix and then find the determinant
then solve for a.
oblique swallow
only 1 question sir, why not the way I was thinking-
austere cove
I honestly don't understand what you were trying to do.
oblique swallow
I honestly don't understand what you were trying to do.
Sooo first we factor out M^2
We get a cubic?
Now the cubic is perfectly aligned with the formula- so we can just calculate for da trace?
why would that not work?
austere cove
I don't know, because I'm not familiar with the technique you are attempting to use.
oblique swallow
I don't know, because I'm not familiar with the technique you are attempting to ...
ahh-
oblique swallow
so we're left with det(M^2 - 3M - 2aM + 8aI - 4I) = 0
welp this would be longer than wat I am thinking of- since I would need to calculate M^2
austere cove
well, give it a go.
oblique swallow
well, give it a go.
i will try ur method, tysm sir
But if anyone can pls tell why method won't work then pls do
austere cove
No, I meant try your method
I just tried my method, and it's pretty gross
there's probably a trick, and if you were taught about something in class then you probably will need to use it.
oblique swallow
there's probably a trick, and if you were taught about something in class then y...
I learned bout this formula like an hour ago- so I dont know how to use it well too...
austere cove
well, unfortunately, I do need to go for now though
oblique swallow
well, unfortunately, I do need to go for now though
alrighty sir! tysm for ur time!
welp I do get the correct answer-
But like it's suspicious
Gemini takes 50 seconds to calculate the same question which I calcculated in less than 2 seconds
I must be doing something wrong?
tiny wharf
can someone please help with this?
quaint jasper
can someone please help with this?
Have you tried using the gradient?
tiny wharf
i am not sure if i know what that is, we are supposed to use the lagranjian method
fallow coral
you would have to find the gradient to use the lagrangian method
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tiny wharf
oh i think i know what you mean
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sterile widget
help
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sterile widget
nvm
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sterile widget
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sterile widget
i dont understand why this is the answer
narrow ermine
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thin monolith
holdon
when you divide in polar form, you subtract the angles
but the angle of 3(1+i) and 5(1+i) are the same, but the angles are not 1 and they are not i either
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gilded fiber
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gilded fiber
i understand that this one is one to one
but i dont know how to prove it
doing f(x1) = f(x2) results in x1^2 = x2^2 where x1 can = -x2 which is a contradiction
but that case is not covered in the domain but idk how to show that
fiery hemlock
I don't think that it is one-to-one
gilded fiber
if the domain was all real numbers it wouldnt be one to one but the domain is all integers
and there isnt any integer inputs that share an output
fiery hemlock
oh, maybe you're right
gilded fiber
and idk how to "prove" that
im 95% sure that this function is indeed one to one but i am struggling how to show that with a proof
because the formula f(x1) = f(x2) does not show x1=x2 since in the real number domain this function isnt one to one so what do i do lol
gilded fiber
wym
fiery hemlock
if f(x)=f(y) for x != y, then our equation is:
$2025x^3-2025y^3=2663x-2663y\$
$2025(x-y)(x^2+xy+y^2)=2663(x-y)\$
Now as we assumed x != y, we can divide by (x-y) and so,
$2025(x^2+xy+y^2)=2663\$
$x^2+xy+y^2=\frac{2663}{2025}$ but x and y must be integers.
glossy valveBOT
Muhammad Saram
fiery hemlock
makes sense?
fiery hemlock
2663 is prime, so you can't divide it by 2025
simply 2663/2025 is non-integral.
vestal moat
Yes also
fiery hemlock
and about onto, I think it's definitely not onto.
gilded fiber
yea
how do i prove that part
just counterexample?
like say there is no x for f(x)=1 or is that not considered a good enough propf
fiery hemlock
like say there is no x for f(x)=1 or is that not considered a good enough propf
I think that's like saying f is not onto 😅
vestal moat
I think that's like saying f is not onto 😅
Here you can use the fact that it has a maximum
fiery hemlock
f?
gilded fiber
a maximum?
vestal moat
My bad it doesn't
for f(x) = 0
you get 2025x^3 = 2663x
2025x^2 = 2663
which is impossible
fiery hemlock
from 2 the f is increasing in positive, just find the point in negative from where it starts decreasing in negative.
wait, lemme get a calculator
i.e also -2
and we never get f(x)=1
@gilded fiber makes sense?
gilded fiber
hmm
fiery hemlock
saying f(x) is never 1 wasn't enough imo, but stating that from 2 it's increasing and from -2 it's decreasing should be enough
gilded fiber
im still a little confused
decreasing and increasing functions can still be onto
or ?
i understand wym but how should i like write that on a test
fiery hemlock
yeah but not the ones which skips a lot of values 😅
fiery hemlock
i understand wym but how should i like write that on a test
that's what I just said
first state that f is increasing from 2 and decreasing -2, not very hard to formally state, right?
And so we never get f(x)=1.
fiery hemlock
np, I think you should close the ticket now
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silk epoch
for the dedekind zeta function over a cyclotomic field, does the product go over all dirichlet characters modulo n, even those induced from smaller moduli, or only the primitive characters?
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frosty gyro
when showing this, would I consider even and odd case and then find out what it converges for both cases and then say the ratio test oscilliates between these 2 limits meaning its indecisive or can I just skip that and say this series oscillates so the ratio test is indecisive
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lime ether
when showing this, would I consider even and odd case and then find out what it ...
i mean what is your statement of the ratio test
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scarlet nacelle
Yo
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amber python
Could someone help me with my math afterschool it is 1 41pm for me maybe around 7 or 8 pm? So ina couple of hours pease I'm in applied math so it not like hard but to me it is, and gr 10
devout valley
As in you want help at that time? You can always come and ask questions you have at that time, and anyone who is available and willing to help then will help you 
You don't have to e.g. arrange anything, just come when you're ready 
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amber python
.reopen
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gritty rose
As in you want help at that time? You can always come and ask questions you have...
did you see this
amber python
How do ik if its open
surreal sand
just open it later then
surreal sand
why do you need to open it in advance
surreal sand
yeah just open it when you are free
gritty rose
You don't have to e.g. arrange anything, just come when you're ready <:happyCat:...
chartbit told you here.
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silk rock
Find an infinite group ( G ) in which every element different from the identity has order ( 2 ).
glossy valveBOT
Halex
rapid rain
Do you know some groups (not necessarily infinite) where this is true?
It can be as simple as you want
rapid rain
Yeah
That's a good start
Now I saw you tinkering with the cartesian product
There's some good ideas behind that
Now let's try using the cartesian product
To make some group bigger than Z2
Where the property is still true
silk rock
but it has to be an infinity group
silk rock
Z_2 x Z_2 ?
rapid rain
Yeah!
Since every element of that group can be written as (x,y)
All I could ask to make it an element of order (at most) 2
Is for both x and y to have order at most 2
And now I hope you can start seeing where we're going
What if I wanted some group bigger than Z2 × Z2
silk rock
so, the infinity group I am looking form looks like $Z_2 \cross Z_2 \cross Z_2 \cross \cdots$
glossy valveBOT
Halex
rapid rain
Yes
silk rock
wow
rapid rain
That would be some form we would like
silk rock
how do one show every elemet has order 2?
silk rock
That would be some form we would like
wdym?
rapid rain
wdym?
Like Z2 × Z2 × ... infinitely is the idea
But were gonna need some rigorous definition
silk rock
But were gonna need some rigorous definition
Is there a simpler group we can work with
rapid rain
All the easy groups I can think of are just different types of "infinite cartesian products" of Z2
rapid rain
But were gonna need some rigorous definition
The best way to find a good definition
Is to start by looking at the finite iterations examples
So we started with Z2
Then Z2 × Z2, which is (Z2)²
Then (Z2)³
... (Z2)^n
Etc...
silk rock
$\prod_{n = 1}^{\infty} \mathbb{Z}_2$
rapid rain
In times like these you have to remember (if you didn't know about this learn it now) the parallel between X^n and the set of functions from {1,...,n} to X
X^n is just a set of lists (x1,...,xn) where each thing in the list is an element of X
So, if you have a function f:{1,...,n} -> X
rapid rain
$\prod_{n = 1}^{\infty} \mathbb{Z}_2$
Uh not sure about that
Maybe remove the n exponent
glossy valveBOT
Halex
rapid rain
And I'm not sure it's the best thing to dabble with infinite cartesian products for now
At least written like this
silk rock
Ohh
rapid rain
So, if you have a function f:{1,...,n} -> X
Let me just continue from there
rapid rain
So, if you have a function f:{1,...,n} -> X
Then all the information I need to reconstruct this function is f(1),f(2),...,f(n)
If I put all of those in a list
(f(1),...,f(n))
Well would you look at that
An element from X^n
This is how we find out that X^n and the set of functions from {1,...,n} to X
Are in perfect correspondance
We say they're isomorphic
rapid rain
So
rapid rain
So we started with Z2
Now this iteration process
Can be seen as starting out from the set of functions {1}->Z2
Then {1,2}->Z2
... {1,2,...,n}->Z2
How do we make it become infinite?
We take the set of functions from ??? to Z2
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silk rock
We take the set of functions from ??? to Z2
Natural numbers?
rapid rain
Natural numbers?
Yes!
No pun intended, this is the most natural set to think about
So let G = set of functions from N to Z2
Can be written as $\mathcal F (\bN,\bZ_2)$ or $(\bZ_2)^\bN$
glossy valveBOT
rafilou is not not born in 2003
rapid rain
Can you guess the operation we will give to this group?
If f and g are both elements of g, how do I define f+g?
silk rock
Can you guess the operation we will give to this group?
f(n) = (Z_2)^n
Wait no
So, the operation should be composition?
rapid rain
?
silk rock
Nvm that
rapid rain
I said that $(\bZ_2)^n$ and $(\bZ_2)^{{1,...,n}}$ were in bijection
glossy valveBOT
rafilou is not not born in 2003
rapid rain
Not N and Z2
Maybe to better understand the operation on G
What's the operation that you put on (Z2)^n?
silk rock
Sum modulo 2
rapid rain
Yeah
Each component is summed mod 2
so like in two dimensions
Z2 × Z2
(a,b) + (c,d) = (a+c,b+d)
If we switched to the "function" way to write it
We would have (f+g)(1) = f(1) + g(1)
And (f+g)(2) = f(2) + g(2)
It's easy to generalize that to:
(f+g)(n) = f(n) + g(n) for all n
"+" here being sum mod 2 ofc
silk rock
It's easy to generalize that to:
(f+g)(n) = f(n) + g(n) for all n
f and g have to be an homomorphism?
rapid rain
f and g have to be an homomorphism?
Well N is not really a group to begin with
So no
They're just regular functions
And we define an operation to sum them up
We just sum up "output-wise"
If you want the output of n by my new function (f+g)
You just add the outputs f(n) and g(n) together
silk rock
Is G a group with what operation? Usually sum of functions?
rapid rain
Something for you to know
If (H,*) is a group
And S is any set
Then $\mathcal F(S,H)$ is a group
glossy valveBOT
rafilou is not not born in 2003
rapid rain
If you define $(f*g)(s) = f(s)*g(s)$
glossy valveBOT
rafilou is not not born in 2003
rapid rain
This is a very standard group creation
That you need to learn from now on
We only need the codomain to be a group
silk rock
Then $\mathcal F(S,H)$ is a group
What operation? Honestly I have not seen these results as of yet, so they look a but confusing to me
rapid rain
**rafilou is not not born in 2003**
This is the operation
The operation for the function group only depends on the operation for the codomain group
rapid rain
What operation? Honestly I have not seen these results as of yet, so they look a...
Take some time to think about it
Here, another example
Since $(\bR,+)$ is a group
glossy valveBOT
rafilou is not not born in 2003
rapid rain
Consider the set $\mathcal F(\bR,\bR)$
glossy valveBOT
rafilou is not not born in 2003
rapid rain
And for $f,g\in \mathcal F(\bR,\bR)$
glossy valveBOT
rafilou is not not born in 2003
rapid rain
I define $f+g$ by: $\forall x\in \bR, (f+g)(x) = f(x) + g(x)$
glossy valveBOT
rafilou is not not born in 2003
rapid rain
So taking f = sin and g = cos for example
sin+cos makes sense as a function
Given by sin(x)+cos(x) for all x
To get f+g of some input
I feed both f and g with the same input
And then add them together
Gonna have to go, ping helpers if you need help to finish this or understand more of what I said
You can probably skip over why F(N,Z2) with + (mod 2) is a group
Try at least to prove the main result
That it's infinite (should be easy) and that every non neutral element is of order 2
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hoary hatch
despite the glaring issues, is this still technically correct?
umbral dome
no, there are several algebra errors
hoary hatch
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craggy torrent
What is the formula for average velocity
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What is the formula for average velocity
umbral dome
average velocity = displacement / time elapsed
onyx glen
What is the formula for average velocity
Google is your friend i think
craggy torrent
Ok
onyx glen
but also that
pure basin
Ann why
pure basin
oh..
craggy torrent
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pure basin
i mean total
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torn jolt
my answer
torn jolt
book's answer
have i gone wrong somewhere so far?
i'll find the constant but idk if i've done it right
actually the constant is 0 doesn't matter
still feel like i've gone wrong somewhere
yeah there's a difference of 4 digits
for q = 100
between the two equations
tf did i do wrong
devout valley
(I at least agree with your integral though there may be missing context that I don't know about - is the revenue just the integral?)
devout valley
Hmm, well the expressions, I don't think they're equivalent 
devout valley
,w int 4/(1 + x)^2 + 2/(1 + x) + 3
glossy valveBOT
devout valley
(that 3 is irrelevant, just include it in the constant)
torn jolt
yes
i could guess as much
BUT LIKE
:iupWE;FOweijufowEIJF
university book btw
sick book btw
thank you uni
yeah well it is what it is
thank you
i was about to start screaming
😭
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smoky rover
dibs
smoky rover
So I am trying to understand this conversion from a+ib from to exponential form
(-i)/(2sqrt(2)(1+i)) = 1/2i times e^(-ipi/4)
I don't think this result is correct
I was trying to write this but it seems better If I just share the picture.
Is this residue result when converted to exponential form correct?
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swift ginkgo
I did this wrong, but have no idea where I went wrong.
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I did this wrong, but have no idea where I went wrong.
crude kayak
I did this wrong, but have no idea where I went wrong.
,rccw
glossy valveBOT
crude kayak
please rotate your picture, so that it's easier for PC users to view it
swift ginkgo
Sorry, i will next time
I figured it out on my own, no need for help anymore.
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torn jolt
Need to find EDC
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Need to find EDC
dawn gazelle
Need to find EDC
so you want to check if it is correct
torn jolt
No no EDC is not 54 EDA need to find EDC
dawn gazelle
ahh you have ADC angle as 54
narrow path
yeah its correct so far
dawn gazelle
ye
torn jolt
ahh you have ADC angle as 54
Yes and I need to find EDA to find EDC
dawn gazelle
ok so we got that AD=BD
torn jolt
Yes yes
dawn gazelle
what if you drew a vertical line from D?
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torn jolt
what if you drew a vertical line from D?
Wait hold on if I do it it’s gonna divide the 126 to 63 and the angel DEB gonna become 27 well there is something wrong
And EDA just becomes 0 degree
torn jolt
Angle FDA is 36 degree
torn jolt
ahhh mannn
Yes what happened
narrow path
"But the problem is in chinese maybe"??
torn jolt
"But the problem is in chinese maybe"??
Definitely
narrow path
There is solution but we cannot see it
i got here through basic methods and i cant see any further
torn jolt
i got here through basic methods and i cant see any further
Dang it the answer is 57 and the angle between is 3 degree
narrow path
Dang it the answer is 57 and the angle between is 3 degree
yeah i know i got there using circles lol and i have no clue how you find it regularly
torn jolt
yeah i know i got there using circles lol and i have no clue how you find it reg...
Bro the answer sheet
narrow path
Bro the answer sheet
what page of the book is this
narrow path
You mean the answers?
i mean what section is it
or like what page is the question on
torn jolt
Oh okay 114
torn jolt
yeah no clue even in the book
Damn(
I solved problems indicated with starts which means hard but this problem has no sign at all bruh
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molten wadi
Does someone know what the letter means in subscript notation for sequences. I understand the n refers to the term but the I dont know what the other one means.
umbral dome
a is the name of the sequence
like in f(x), x is the input and f is the name of the function
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chrome ore
=vector 0
austere cove
@chrome ore it might help the helpers if you disclose the solution to question 1.
chrome ore
I don’t have it on me
You just replace M with A and M’ with A’ and find a relation vetween AA’ and AB
Then the same thing with B and B’
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chrome ore
<@&286206848099549185>
west lance
Rewriting with position vectors could help
Also midpoint of MM' is interesting
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weak flame
wazzup beijing, missed the first day of the new unit and i have no idea what this homework is
leaden ermine
wazzup beijing, missed the first day of the new unit and i have no idea what thi...
the domain is what values of x are allowed to input
for square roots you have to keep in mind that what's inside must be positive or 0
for graphing do a table
and plot the points
fleet swift
yup
weak flame
can we keep in mind this is the first time im ever seeing any of this
fleet swift
you studied square roots before?
weak flame
like a while ago i think yeah
fleet swift
its the inverse function of power of 2
so when u put something to the power of 2
to go back to the expression before the power u put the square root
so as you know the number u get from the power of 2 is always positive
thus what u put under the square root will always be positive
so this is the rule
x+4 must be positive
weak flame
ok
fleet swift
and for it to be positive x+4>0 means x>-4
leaden ermine
(it can also be 0)
fleet swift
it can be equal to zero too
fleet swift
yes
there are imaginary ones too
but i dont think u studied them yet
in complex numbers the square root can be negative
weak flame
doesnt that just mean theres no real roots
fleet swift
just so you know ;0
weak flame
can we graph it first
fleet swift
sure choose values that fall into the domain
weak flame
what
fleet swift
(you cannot graph without knowing the domain)
weak flame
whats the domain
fleet swift
because the domain is where the function exists
once u go outside it then you changed the function
each function has its domain
where it exists and can be drawn in other words
weak flame
what is domain bruh
weak flame
the domain is where the function exists
what does that mean
fleet swift
do you know what a function is
weak flame
probably do but dont know the name
fleet swift
the domain is all the values of x that u can plug in and then get an answer
weak flame
ok yeah that makes alot more sense
weak flame
sure choose values that fall into the domain
ok then back to this point how would i find values that fall into the domain
fleet swift
by looking for the conditions that need to be met
i told you the square root can only have positive values under
thus thats the rule
for what is under the sqrt to be +
fleet swift
you determine the domain...
weak flame
yeah dont know how to do that
fleet swift
you conclude from my words
x+4 needs to be
positive
honestly i cannot explain this by just typing, you need to watch the lesson and learn the basics
then if u have a question feel free to ask me
weak flame
domain isnt like 1 singular number?
fleet swift
no
like imagine u have an ice cube
for it not to melt there is a range or temperatures than should not be surpassed
like under 5C for example
so for the ice cube to exist the temperature should be under 5
or it ll melt
it can be 3, 2, -10, 5/2, -50...etc
weak flame
bruh i dont get it
ima watch a khan academy video on this
or like
some random 12 year old video by an underappreciated math teacher who video copies his lessons
fleet swift
ima watch a khan academy video on this
yes
weak flame
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brittle cliff
should I be doing some kind of sum here or just estimating?
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should I be doing some kind of sum here or just estimating?
leaden ermine
should I be doing some kind of sum here or just estimating?
given the table it seems sum
leaden ermine
there is just one sum
royal holly
given the table it seems sum
There is a pattern to guess the function, but I don’t think that is ideal.
brittle cliff
but like which method of summing
leaden ermine
you are basically summing up the area of the rectangles
they all have a constant with Delta_x = 0.5
brittle cliff
do i do left riemann, right riemann, midpoint, trapezoid? which one?
brittle cliff
im getting 77 but the answer is B
steel solar
do i do left riemann, right riemann, midpoint, trapezoid? which one?
Probably right, it will provide an under approximation
brittle cliff
left sum gives 50 and right gives 77
but the answer is B
is it like we dont know exact value so were chosing some value in between those?
leaden ermine
no the task is ambiguous
you can try now some mid point shit as well and hope to get 62
leaden ermine
i tried mid point and got 63.5 skull
brittle cliff
terrible problem
steel solar
Trapezoidal it is
uncut badge
????
umbral dome
you have to follow the right hand rule
uncut badge
i did
i dont understand it cuz i follow one video and get it correct
but khan academy is on different shit
i dont understand why they curl their fingers
umbral dome
well no matter what version of the right hand rule you should get the same result if you follow it correctly
uncut badge
why is it -(Bxv) ?
umbral dome
can you show the version of the right hand rule you are using?
uncut badge
this is what i chose ^ but the correct answer is this v
cuz i did get this
but i reversed it
umbral dome
why is it -(Bxv) ?
that's just what the question is asking for
uncut badge
and got my answer as the negative
umbral dome
you should follow the general right hand rule for cross products
not a specific right hand rule for magnetic force
uncut badge
do you have a video for that
umbral dome
because the magnetic force is given by F = qv x B, but in the question they ask about B x v which will have the opposite direction
uncut badge
why will it have the opposite direction
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astral belfry
how am i supposed to contort my hand to this
Carefully
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sharp osprey
hi
sharp osprey
convergence and divergence tests
i dont like them at all, and i never know when to use which one, or very rarely do I, partially a problem with lack of practice but also I think it is something else
when I talk to people who seem to know which one to use and when
they seem to have some kind of intuitive understanding, or educated guess, if the function will diverge or converge before they apply any tests
thick hedge
This is how it should work
velvet sedge
there is a sort of pipeline you can apply
sharp osprey
but the ones i asked had a hard time explaining exactly how they have this educated guess
velvet sedge
its not exactly perfect but i do think it is nice, the pipelkine i mean
sharp osprey
i have seen flow charts online
thick hedge
after that , you can apply convergence tests
sharp osprey
but i wanna be able to try less tests and just get to the right one asap
thick hedge
if there's a factorial, use the ratio test
if there's exponents, use the root test
if it looks like an integrable function, the integral test
if it looks like a modified p-series , comparison
velvet sedge
well, in general, if you see constant/(expression that increases) and you're summing it, you know it will fail the divergence test, and same goes for slower growing expression/faster growing expression
thick hedge
if it's alternating, you first check for absolute convergence, and if that doesn't work, you use the alternating series test
I think that covers everything
?
sharp osprey
sorry how do i see that it is alternating again?
is it when it is ^3?
somewhere?
and a negative number?
velvet sedge
alternating has negative and positives
thick hedge
like (-1)^n/n is an alternating series
velvet sedge
so if you have some trig function(n) or (-1)^n or smth along those lines
sharp osprey
okay that makes sense
thick hedge
ofcoursse if you have something like \sqrt{n}/n+k , don't use the divergence test, directly comparison
sharp osprey
for the comparison test, am i comparing it to an unmodified p-series?
thick hedge
for the comparison test, am i comparing it to an unmodified p-series?
usually
at times other series can help too
sharp osprey
im kind of upset by these tests because i have been trying to get away from memorizing things in math
did you guys memorize them
or can you kind of understand why they work?
and like recreate the test
if you forget them
i've had a really hard time memorizing the ones that use limit
thick hedge
or can you kind of understand why they work?
Try to understand them first
thick hedge
atleast intutuvely
sharp osprey
okay yeah i dont understand them at all i just jumped on memorizing them immidietely
thick hedge
Atleast get the intution
the proofs can wait for an anlysis course( perhaps)
@velvet sedge can add to this, I think moosey knows more than I do
velvet sedge
and like recreate the test
yeah you can 'prove' these tests work, this is part of what real analysis is about
sharp osprey
the course im taking is called single variable analysis but i dont think us engineering students are really required to prove any of them
sharp osprey
ok ty i will check it out
there is probably too much to add seeing how broad my original question is
velvet sedge
its very very user friendly and they talk through a lot of the material
sharp osprey
okay thanks Moosey, can I ask one last question here
velvet sedge
sure
sharp osprey
that is more specific and tbh, only tangential to these tests
(n+1)! can be simplified to (n+1)n!
but i dont remember why
while using the ratio test i think
i encountered that
thick hedge
(n+1)! can be simplified to (n+1)n!
(n+1)! by definition is the product of all (natural (_numbers from 1 to (n+1) inclusive
n! is the product of all numbers until n
thick hedge
for (n+1)! , n=2, yes
sharp osprey
is that the same as 3!?
sharp osprey
6
thick hedge
okay
sharp osprey
okay so
(n+1)n!
was the same, somehow
so i get
(3)2!
OOPS
did i already go wrong
sharp osprey
(3)2!
with this
wait
3 times 2!
that is 6
that feels like black magic
(4)! = 4! = 24
(4)3! = 4*6 = 24
that's not okay
but thank you
i don't like that
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steep vigil
Can someone help me answer question 4b ( I don't understand what the question is asking.
bitter beacon
find all x when the function is positive, that's what it means
steep vigil
so when it is above y=0 ?
sacred cloak
Can someone help me answer question 4b ( I don't understand what the question is...
Find the set of all x for which the given expression is above 0
steep vigil
Find the set of all x for which the given expression is above 0
So basically find values of x where it is greater than 0 right?
x>3 ?
@sacred cloak
Like this ?
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onyx glen
Like this ?
you should not be writing $\in$ like a big capital E
glossy valveBOT
Ann
onyx glen
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✅
onyx glen
yeah that's better
tho i would say it needs to be a bit flatter
the same-ish height and placement as a plus sign
rare pine
If 729^x +27^y = 3140, and 2x+y = 4, what is the value of 3^2x + 3^y?
rare pine
i have this (where A = 3^2x + 3^y) but i dont think this has integer solutions..? or did i do something wrong
holy shit im so washed
sorry guys 😭
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daring terrace
could someone pls assist me with this question? my working out has been uploaded asw at where im at
onyx glen
1000 = 8*125
onyx glen
your handwriting is a bit eh
daring terrace
oh sorry i was rushing
daring terrace
1000 = 8*125
oh ye true
mb
wait so after that i do the opposite right coz its iff
i start with 1000x+100a+10b+c = 8K
modest obsidian
i start with 1000x+100a+10b+c = 8K
the 1000x is kinda unnecessary because it's THREE DIGITS
daring terrace
the 1000x is kinda unnecessary because it's THREE DIGITS
oh rlly? but they didnt define how many digits the whole number is can we just assume its 3
coz of the statement
modest obsidian
just generalise that any >3 digit is a multiple of 1000 = 8*125 so divisible by 8 for assuming any arbitrary number
then only focus on the 3 digit or less bit
glossy valveBOT
parabolicinsanity
modest obsidian
that's all
onyx glen
the 1000x is kinda unnecessary because it's THREE DIGITS
nope
the x handles the rest of the number
modest obsidian
i thought it was for the other way around 😔
3 digits divisibility to entire number divisibility
modest obsidian
yes
daring terrace
but how do i go from 1000x+100a+10b+c = 8K to xabc = 8A or something
coz i need to go from the last three digits being divisible by 8 to the whole number being divisible by 8
modest obsidian
$a\mid b \land a\mid c \implies a\mid bx+cy, \forall (x,y)\in \mathbb{Z}^2$ just use this i guess
glossy valveBOT
parabolicinsanity
modest obsidian
something like that
daring terrace
what is that-
modest obsidian
for q to p implication
daring terrace
ive never seen that in my life
modest obsidian
basically if
a divides b
and b divides c
then for any two integers x,y
a divides bx+cy
i thought you were doing number theory from the looks of it
since from q
uhh
8 divides the first 3 digits
and since 1000 is divisible by 8
that means 1000x + three digits = the number is divisible by 8
and then you have your proof
do you follow? @daring terrace
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modest obsidian
happy mathing
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teal path
Can someone explain my why in convolution when we have 2 functions suppose x(t)=t^2 and h(t)=e^t and we apply the convolution formula ∫x(τ)*h(t-τ)dτ we don’t substitute back the shifted value in h(t-τ) and as I have seen we just adjust the limit integration and that makes me confused.
I mean how is it shifted the h(t-τ) without plugging into to the t the value we are shifting.
west lance
Can someone explain my why in convolution when we have 2 functions suppose x(t)=...
here t is fixed, so t is the shift, or im missing something?
teal path
here t is fixed, so t is the shift, or im missing something?
Yes t is the shift but in integration we don’t plug in the value t it’s shifted by
west lance
Yes t is the shift but in integration we don’t plug in the value t it’s shifted...
because in this integral t is fixed so its not changing (for integral its just parameter)
teal path
because in this integral t is fixed so its not changing (for integral its just p...
could you elaborate further ?
I have seen in all cases they never plug in the t the value which h(t) is shifted by
west lance
because (x * h)(t) = ∫x(τ)*h(t-τ)dτ is function of t, its not a value
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teal path
because (x * h)(t) = ∫x(τ)*h(t-τ)dτ is function of t, its not a value
Yes so
west lance
Yes so
this is convolution. its not some value the result is function of t, or you asking something else?
teal path
I’m asking why don’t we plug in h(t) the value we’re shifting the h(t)
west lance
can you show me example not sure if i undersand you
torn jolt
Find dy/dx
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# **Find dy/dx**
spiral elk
# **Find dy/dx**
2x(x+3) is the error
onyx glen
... yes
you kind of skipped a step
it would be better if you wrote $\frac{x}{2\sqrt{x+3}} + \frac{2(x+3)}{2\sqrt{x+3}}$ and only then $$\frac{x + 2(x+3)}{2\sqrt{x+3}}$$ and then it would not have occurred to you to multiply the numerators
glossy valveBOT
Ann
onyx glen
# **Find dy/dx**
also try to be consistent in how you write your x's. only like half of the x's you wrote look like actual x's
the other half look like n's or u's or whatever else but not x
so like, be consistent and always write the good-looking x's, yeah?
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analog tendon
How would i start preparing for international math modelling competition???
I am in grade 11 rn need beginner book to make my foundation strong
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I am...
@analog tendon Has your question been resolved?
thorn marten
Find the sum of all the unique combinations pq, where 1 <= p, q <= n.
thorn marten
Is it clear what is being asked?
foggy vapor
Do you mean like
[
S(n) =\sum_{1\le p\le q\le n}pq
]?
thorn marten
p * q
glossy valveBOT
Aero
thorn marten
Like (1 * 2 + 1 * 3 + 1 * 4............ + 1 * n) + (2 * 3 + 2 * 4 + 2 * 5 + .............. + 2 * n) ........
grave elm
idk how to give you a hint without revealing too much
thorn marten
Also, p neq q
grave elm
let's be a bit more general, say you wanna find out
ab + ac + ad + bc + bd + cd (so all possible products of 4 numbers a, b, c, d)
can you find an expression, which when expanded involves those terms in some way?
and dont worry if theres something extra
onyx glen
so $\sum_{1 \leq p < q \leq n} pq$ then
glossy valveBOT
Ann
onyx glen
is that what you're looking for @thorn marten
thorn marten
I am not sure.
S(n) = [1 * 2 + 1 * 3 + 1 * 4 + 1 * 5 + ............. + 1 * n] + [2 * 3 + 2 * 4 + 2 * 5 + 2 * 6 + 2 * 7 + ....... + 2 * n] + [3 * 4 + 3 * 5 + 3 * 6 + 3 * 7 + ....... + 3 * n] ..........
On expansion this should come.
onyx glen
that's what this sum works out to.
... i thought i witnessed you at least become familiar with sigma notation
thorn marten
Can't we simply write (cyc) below the sigma symbol?
onyx glen
mmm
no, that would be quite sus out of context
and your sum's not cyclic
ok actually here's something
this is \textbf{not} the same as your sum, but there is in fact a connection:
do you know how to calculate $\sum_{k=1}^n k^2$?
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Ann
grave elm
Is this what you are looking for?
thorn marten
S(n) = [1 * 2 + 1 * 3 + 1 * 4 + 1 * 5 + ............. + 1 * n] + [2 * 3 + 2 * 4 + 2 * 5 + 2 * 6 + 2 * 7 + ....... + 2 * n] + [3 * 4 + 3 * 5 + 3 * 6 + 3 * 7 + ....... + 3 * n] ..........
= 1(2 + 3 + 4 + 5 + .... + n) + 2(3 + 4 + 5 + 6 + ......... + n) ......
= 1[n(n+1)/2 - 1(1+1)/2] + 2[n(n+1)/2 - 2(2+1)/2] + .......... + k[n(n+1)/2 - k(k+1)/2] + .......... + (n-1)[n(n+1)/2 - (n-1)n/2] + (n)[n(n+1)/2 - n(n+1)/2]
= sum from k = 1 to k = n of
k[n(n+1)/2 - k(k+1)/2], where n = constant in the expression.
grave elm
S(n) = [1 * 2 + 1 * 3 + 1 * 4 + 1 * 5 + ............. + 1 * n] + [2 * 3 + 2 * 4 ...
not that something like this wouldnt work, but it's extremely tedious
onyx glen
Is this what you are looking for?
kinda
onyx glen
S(n) = [1 * 2 + 1 * 3 + 1 * 4 + 1 * 5 + ............. + 1 * n] + [2 * 3 + 2 * 4 ...
per aspera ad astra, huh?
onyx glen
@thorn marten take note of this.
thorn marten
oh
onyx glen
do you see what i'm getting at here?
thorn marten
yes
onyx glen
there's an equality that i wrote down but blurred in this photo
thorn marten
Well the sum of all the terms in the square = (n(n+1)/2)^2
The diagonal divides it into two parts with an equal area. The diagonal = n(n+1)(2n + 1)/6
onyx glen
eh.
i wouldn't speak of area.
you can view it as such but from my POV it's just a table of numbers.
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thorn marten
let's be a bit more general, say you wanna find out
ab + ac + ad + bc + bd + cd ...
I get it now.
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amber leaf
what are the odds of getting a 1 in 50 million pet if I have 25x luck and 2450% luck
sharp lagoon
Do you have a formula for what luck has to do with it?
narrow path
literally applied math
lost topaz
Do you have a formula for what luck has to do with it?
this^
cause it depends at what applies first
amber leaf
Do you have a formula for what luck has to do with it?
No its a game
granite torrent
what are the odds of getting a 1 in 50 million pet if I have 25x luck and 2450% ...
0.001225% if both of these multipliers are multiplicative
rain merlin
||i think you should express it as 1 in a ___||
fathom saddle
We have no idea what the word "luck" means here. That's not a common mathematical thing.
amber leaf
0.001225% if both of these multipliers are multiplicative
alright thanks
fast peak
its unclear how they are applied. like if you had 50 million times luck, would it then be guaranteed? or just much more likely
amber leaf
its unclear how they are applied. like if you had 50 million times luck, would i...
just more likely
amber leaf
yes it is
rain merlin
is it like for every n luck it goes 2^n
amber leaf
yes
rain merlin
because it depends right
amber leaf
0.001225% if both of these multipliers are multiplicative
I think this guy is correct
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rain merlin
that was a fever dream of a help channel
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queen dome
I need help xd
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gritty rose
I need help xd
queen dome
dayum google translate is changing the stuff
wait
ama translate
Given is the function 𝑓 defined in ℝ with 𝑓(𝑥) = −𝑥^2 + 2𝑎𝑥 with 𝑎 > 1.
The zeros of 𝑓 are 0 and 2𝑎.
a) and now I need to show that the Graph f and the 𝑥-axis have the area 4/3a^3
and b) is that:
The vertex (𝑎|𝑎^2) of the graph of 𝑓 lies on one side of a square. Two sides of this square lie on the coordinate axes (see figure). The area of the square is equal to the area of the area enclosed by the graph of 𝑓 and the 𝑥-axis.
Determine the value of 𝑎.
leaden ermine
mit welcher
queen dome
was? mit welcher was?
leaden ermine
ja die a) oder b)?